Question: $A$ $B$ $C$ If: $ AB = 4x + 8$, $ BC = 7x + 3$, and $ AC = 66$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 8} + {7x + 3} = {66}$ Combine like terms: $ 11x + 11 = {66}$ Subtract $11$ from both sides: $ 11x = 55$ Divide both sides by $11$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 7({5}) + 3$ Simplify: $ {BC = 35 + 3}$ Simplify to find ${BC}$ : $ {BC = 38}$